Panel Data Models Analysis
A general
model that pools time series and cross section data is
k
Yit =
k=0
where i=1,…, N
(number of cross sections, e.g., countries); t=1,…, T (number of time periods,
e.g., years); and K = number of
explanatory variables. Note that this model gives each state its own intercept.
Let suppose Pakistan have high growth rate holding other thing constant so this
model allow each year have its own effect (βt).
Different models
are derived by making various assumptions concerning the parameters of this
model. If we assume that α1 = α2 = = αN,
β1 = β2 = βt … , and γ1,k = γ2,k = = γN,k … then we have the OLS model.
If we assume
that the αi and βt not all equal but are fixed numbers (and
that the coefficients i,k are
constant across countries, i) then we have the fixed effects (FE) model. This model is also called the least squares dummy variable (LSDV) model, the covariance model, and the within
estimator. If we assume that the αi and βt are random variables, still assuming that
the γi are all equal, then we have the random
effects (RE) model also known as
the variance components model or
the error components model. Finally,
if we assume the coefficients are constant across time, but allow the k, αi and
k, γi to vary across countries and assume that βt = = βt = 0… , then we have the random coefficients model.
The Fixed Effects Model
Let’s assume
that the coefficients on the explanatory variables k,i,t
x are constant across countries and across time.
The model therefore reduces to
k
Yit =αi +βt ∑ γk Xk,i, t + ℰi, t
k=0
i will explain fixed effect model with dummy variables in next blog.....nshallah
